Schützenberger groups ofH-Classes containing odd degree polynomials-Classes containing odd degree polynomials

In this note we determine when topological simplicity of a subsemigroup implies its simplicity. A measure theoretic approach is used. The main result is: In a locally compact completely simple semigroup whose maximal subgroups are compact, every subsemigroup which is either locally compact or of non-empty interior is completely simple. As a corollary, we have: In a compact semigroup, any topologically simple subsemigroup which is either locally compact or of non-empty interior is simple.     

Spectral decomposition of the tent map with varying height

The generalized spectral decomposition of the Frobenius-Perron operator of the tent map with varying height is determined at the band-splitting points. The decomposition includes both decay onto the attracting set and the approach to the asymptotically periodic state on the attractor. Explicit compact expressions for the polynomial eigenstates are obtained using algebraic techniques. (c) 1998 American Institute of Physics.     

Experimental and Theoretical Insights into the Optical Properties and Intermolecular Interactions in Push-Pull Bromide Salts

Experimental and theoretical insights into the nature of intermolecular interactions and their effect on optical properties of 1-allyl-4-(1-cyano-2-(4-dialkylaminophenyl)vinyl)pyridin-1-ium bromide salts ( I and II ) are reported. A comparison of optical properties in solution and in the solid-state of the salts ( I and II ) with their precursors ( Ia and IIa ) is made. The experimental absorption maxima (λ_max) in CHCl₃ is at 528 nm for I and at 542 nm for II , and a strong bathochromic shift of ∼110 nm is observed for salts I and II compared with their precursors. The absorption bands in solid-state at ∼627 nm for I and at ∼615 nm for II that are assigned to charge transfer (CT) effect. The optical properties and single crystal structural features of I and II are explored by experimental and computational tools. The calculated λ_max and the CT are in good agreement with the experimental results. The intermolecular interactions existing in the crystal structures and their energies are quantified for various dimers by PIXEL, QTAIM and DFT approaches. Three types of interactions, (i) the cation⋅⋅⋅cation interactions, (ii) cation⋅⋅⋅anion interactions and (iii) anion⋅⋅⋅anion interactions are observed. The cationic moiety is mainly destabilized by C−H⋅⋅⋅N/π and π⋅⋅⋅π interactions whereas the cation and anion moiety is predominantly stabilized by strong C−H⋅⋅⋅Br⁻ interactions in both structures. The existence of charge transfer between cation and anion moieties in these structures is established through NBO analysis.     

On upper bounds for the growth rate in the extended Taylor-Goldstein problem of hydrodynamic stability

For the extended Taylor-Goldstein problem of hydrodynamic stability governing the stability of shear flows of an inviscid, incompressible but density stratified fluid in sea straits of arbitrary cross-section a new estimate for the growth rate of an arbitrary unstable normal mode is given for a class of basic flows. Furthermore the Howard’s conjecture, namely, the growth rate kc _i → 0 as the wave number k → ∞ is proved for two classes of basic flows.